The electric charges ' +2q ', ' +2q ', ' -2q ' and ' -2q ' are placed… | MHT CET 2025 (21 Apr, Shift 1)

Q33MHT CET 2025 · 21 APR · SHIFT 1Medium

Electric Potential & Equipotentials

The electric charges ' $+2q$ ', ' $+2q$ ', ' $-2q$ ' and ' $-2q$ ' are placed at the corners of square of side ' 2 L ' as shown in figure. The electric potential at point 'A', midway between the two charges ' $+2q$ ' and ' $+2q$ ' is

( $\varepsilon_0 =$ permittivity of free space)

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Answer: (b)

A is at distance $L$ from each $+2q$ and $\sqrt{(2L)^2 + L^2} = \sqrt5\,L$ from each $-2q$ .
$V_A = k\left[\dfrac{4q}{L} - \dfrac{4q}{\sqrt5\,L}\right] = \dfrac{1}{4\pi\varepsilon_0}\dfrac{4q}{L}\left[1 - \dfrac{1}{\sqrt5}\right]$
$V_A = \dfrac{q}{\pi\varepsilon_0 L}\left[1 - \dfrac{1}{\sqrt5}\right]$
So the answer is (b).

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